Problem: Simplify the following expression: $q = \dfrac{4y + 3}{5} \div \dfrac{3y}{5}$
Answer: Dividing by an expression is the same as multiplying by its inverse. $q = \dfrac{4y + 3}{5} \times \dfrac{5}{3y}$ When multiplying fractions, we multiply the numerators and the denominators. $q = \dfrac{ (4y + 3) \times 5 } { 5 \times 3y}$ $q = \dfrac{20y + 15}{15y}$ Simplify: $q = \dfrac{4y + 3}{3y}$